Predicted-Flow Control Barrier Functions for Real-Time Safe Optimal Control

2026-05-29

AI Summary

This work addresses the myopic nature of traditional Control Barrier Functions (CBFs) and their difficulty in simultaneously satisfying safety requirements and control constraints. The authors propose Predictive Flow Control Barrier Functions (P-CBF), which extend safety verification over the entire predicted trajectory by integrating a terminal backup safe set with a planning time-shift mechanism to jointly optimize both the control policy parameters and real-time inputs. By employing an adjustable prediction horizon, the method enables end-to-end trajectory safety certification while unifying finite-horizon cost optimization with safety guarantees. Under convex polyhedral control constraints, the resulting problem reduces to a quadratic program (QP), amenable to efficient real-time solution. Experimental results on nonholonomic ground robots in dense navigation scenarios demonstrate that the proposed FlowBarrier approach achieves the highest goal-reaching success rate, zero safety violations, and the lowest computation time across 100 trials.

Abstract

Control barrier functions (CBFs) provide real-time safety guarantees through pointwise conditions on the state. However, synthesizing a valid CBF is difficult and the resulting controllers are myopic. To address myopia, this article introduces predicted-flow control barrier functions (P-CBFs), which generalize the CBF from a function of the current state to a functional of a predicted flow under a parametrized control plan over a finite prediction horizon. For safety, a P-CBF can certify that the predicted flow is in a safe set over the entire prediction horizon. However, candidate P-CBFs suffer from the same challenge as candidate CBFs, namely, control constraints make it difficult to guarantee that the P-CBF is valid. This article resolves this challenge by introducing a terminal candidate P-CBF requiring that the predicted flow end in a backup safe set at the terminal time, and a planning-time shift that modulates the prediction horizon, providing an additional degree of freedom to ensure feasibility. The real-time control and the evolution of the control-plan parameter and planning-time shift are determined jointly by a single convex optimization that is guaranteed to be feasible and renders the associated safe set forward invariant. The resulting safe optimal flow control provides a safety certificate over the entire prediction horizon and unifies finite-horizon integral-cost optimization with safety certification. This optimization reduces to a quadratic program (QP) if the control constraints are a convex polytope. The QP implementation, termed FlowBarrier, is validated on a nonholonomic ground robot navigating a dense environment. FlowBarrier is compared to nonlinear model predictive control and two CBF-based safety filter methods across 100 trials, where FlowBarrier achieves the highest goal-reaching rate, zero safety violations, and the lowest computation time.

Problem

• Control Barrier Functions
• Real-Time Safety
• Myopia
• Predicted Flow
• Safety Certification

Innovation

• Predicted-Flow Control Barrier Functions
• Safety Certification
• Convex Optimization
• Model Predictive Control
• Forward Invariance